{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$第一节——映射与函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1.函数需满足双射（单射+满射）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2.一个函数有反函数存在的条件是："
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（1）关于y=x对称，且保证为一个函数。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（2）充要条件是函数在它的定义域上是单调的。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（3）性质为：函数与反函数在相应区间上的单调性一致。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（4）偶函数一定不存在反函数，奇函数不一定存在反函数，且奇函数的反函数也是奇函数。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "反正弦函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x = np.linspace(-1, 1, 400)\n",
    "\n",
    "y = np.arcsin(x)\n",
    "\n",
    "plt.plot(x, y, label=r'$\\arcsin(x)$')\n",
    "\n",
    "plt.title('Arcsine Function')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "\n",
    "plt.grid(True)\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "反余弦函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x = np.linspace(-1, 1, 400)\n",
    "\n",
    "y = np.arccos(x)\n",
    "\n",
    "plt.plot(x, y, label=r'$\\arccos(x)$')\n",
    "\n",
    "plt.title('Arccosine Function')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "\n",
    "plt.grid(True)\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "反正切函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Sv9LSUmRlZSEsLAwODi0fLFWpVIiPj8eoUaOs8pRXwPr7yP5ZPmvvI/unv9LSUsjl8haFIZs4THarwYMHY8uWLY2+LpVKIZVK6y0Xi8X1dpRarYZIJIKLi4tec040Gg0AbbCzxjkrltI/qVSqO9NQnz/Ghn43rI2195H9s3zW3kdr61+1So1yRQ2Ky1VILwfyK9XoKK9/9KUtWvPzsrkwdOrUKQQEBBh0m+Y86kHN4/4jImoZjUZAWXUNSqtVKKuuQVm1CuWKGu33ihqU377slue1y8qra6BUa27ZqgOqvDPwjzHdTdYviwpD5eXluHz5su55amoqkpKS4OXlhY4dO2LJkiXIzMzEF198AQBYs2YNQkND0bNnTyiVSmzZsgU7duzAjh07TNUFIiIikxIEARVKNUqqVCiuVKKkSoXSKhWKK1UoqdI+im9+La19fvO10moVDDm5xllqD7FQA5mDaY8eWFQYOnHiRJ0zwRYsWAAAmD59OjZt2oTs7GykpaXpXlcqlVi0aBEyMzPh6OiInj174pdffsG4cePavXYiIiJjqFapUVChRFGFEgUVShRWKFBYobrtqxKFFUpdqKnRtC3RSB3s4CoTw03mABeZA1xlDnCROsBFKobrzefaZdrnLjIHbdtbnrtIHKBW12DXrl0YN7yTgX4a+rGoMDRixAg0Nd9706ZNdZ6//PLLePnll41cFRERkeEIgoDSqhrklVcjq6gCJ/JEyDl0DQWVNcgvU9wMPP97VKn0u46bxN4Obo5ieDiJ4e7Y+OP2190cxZCJ7Q3SV3O5BJ1FhSGybQUFBejevTuOHz+O0NDQFq3z0EMPYciQIbpRRCIiUxEEAUWVKmQVVyGnpBq5ZQrkllUjr0yBvDIFcm9+zStXQFlz65wae+Dy301uW2wvgqeTBF7OEni7SODpJIG3swRezlJ4OYvh5SyFp7MYXs4SbcBxlEAmtuOcyZsYhshgRowYgb59+2LNmjVG2f67776LiRMntjgIAcCbb76JkSNHYtasWc2eWklEpC9BEFBcqUJ2STWyS6r+97W4us4yRZ2Q0zQ3mQPkLlLYKcsQERIIP3dHyF2k8HaRwMtJAi8XbeDxdJbAVerAYNMGDEPUIkqlEhKJxGTvX1VVhbi4OOzatatV6/Xu3RuhoaH46quvMGfOHCNVR0S2oFxRg/TCSqQVViK99lFUhbTCSmQWVbX4cJXcRQJ/dxn83WTwcZXCx0UKHzeZ9qurFL6u2q8ysT1UKpV2Ts243lZ1ar25YRgyMEEQWvwHodFoUKVUw0FZ0+br8DiK7Vv1v4I9e/bgrbfewrlz52Bvb4+YmBh8+OGH6Ny5MwDtKE9kZCQkEgm++OIL9OzZEwcOHIBGo8G//vUvbNiwAenp6fDz88Ozzz6LS5cu4cCBAzhw4AA+/PBDAMCVK1fg5eWFPXv24J133mnyvXr37g2ZTIb/+7//g0QiwezZs7Fs2TJdvbt374aDgwNiYmLq9OPrr7/Gk08+iStXrqBDhw4AgFmzZuH48eP4448/4O7ujkmTJuHrr79mGCKiJgmCgMIKJa7mV+BqXjmuFdQNPYUVyma34eUsQYC7DAHujtqvHjLd80B3R/i6SQ0234YMh2HIwKpUavR4c2+7v++FFaPhJGn57qyoqMCCBQvQq1cvVFRU4M0338T999+PpKQkXTDbvHkz5syZg0OHDukmri9ZsgQbNmzA6tWrcccddyA7OxsXL17EvHnz8PfffyMyMhIrVqwAAHh7e6OioqLF77VgwQIcO3YMR44cwYwZMzB06FCMGjUKAHDw4EFER0fX68eUKVOwcuVKvPvuu1i7di2WL1+OvXv34ujRo3B3dwcADBw4EO+++y4UCkWDF9QkItuiqFEjraASV/IqcDW/HFdytV+v5lWgpKrp+1l5OokR7OWkfXg6IdjLER29nBDk6YQAdxmDjoViGLJRDz74YJ3ncXFx8PX1xYULFxAZGQkA6NKlC1atWqVrU1ZWhg8//BBr167F9OnTAQCdO3fGHXfcAUB793cnJyf4+/sD+N8VqB988ME6I18NvVfv3r2xdOlSAEDXrl2xdu1a/Pbbb7owdO3aNQQGBtbrh0gkwttvv42HHnoIgYGB+PDDD/HHH3/oRokAoEOHDlAoFMjJyUFISEgbfmpEZEnUGgFphZVIySlFcnYZUnLKkHKjDNcLKtDYmeUiERDo7ohOPs4Ikzvrgk5HL23wcZXxUJU1YhgyMEexPS6sGN2ithqNBmWlZXB1czXIYbLWuHLlCt544w0cPXoU+fn5uuCSlpamCyi3j8QkJydDoVDg7rvvbvV7LV26tMn36t27d511AgICkJubq3teVVUFmUzW4PYnTJiAHj16YPny5di3bx969uxZ53VHR0cA2pv2EZF1KqtW4WJayc3QU6oLPtWqhicsu0gd0MnHGZ3kzujk44JOPs7o7OOCMLkzR3dsEMOQgYlEohYfrtJoNKiR2MNJ4tDu9+6aOHEigoODsWHDBgQGBkKj0SAyMhJK5f+OiTs7O9dZpzZUtNa9997b7HvdPjFQJBLpQhMAyOVyFBUVNbj9vXv34uLFi1Cr1fDz86v3eu3d6H18fPSqn4jMS6WyBuezSnEmowSn04pw9G975B7Z32BbqYMduvm5ItzfFRH+rojwd0M3Pxf4uEp59hXpMAzZoIKCAiQnJ+PTTz/FsGHDAAB//vlns+t17doVjo6O+O233zBr1qx6r0skEqhvu4JWYWGhXu91u379+jV4g92//voLkydPxqeffopt27bhjTfewLffflunzblz5xAUFAS5XN7q9yUi0xIEAVfzK3DiWiFOXCvC6YxiXM4tv+0wlzbUdPBwRM9AN0QEuCHCXxuAQr2dYW/H0ENNYxiyQZ6envD29sZnn32GgIAApKWlYfHixc2uJ5PJ8Morr+Dll1+GRCLB0KFDkZeXh/Pnz2PmzJkIDQ3FsWPHcO3aNbi4uMDDwwMeHh56vdftRo8ejSVLlqCoqAienp4AtPOIxo8fj8WLF2PatGno0aMHBgwYgJMnTyIqKkq37h9//IHY2NhWvycRtT9ljQZnM0u04ed6EU5eL2rwLC5/Nxl6BbmjZ4ArqjNTMOO+u+Hv4dzAFomaxzBkg+zs7LBt2za88MILiIyMRHh4OD766COMGDGi2XXfeOMNODg44M0330RWVhYCAgIwe/ZsAMCiRYswffp09OjRA1VVVbpT67du3Yr58+e3+r1u1atXL0RHR+Obb77Bs88+i8LCQowdOxaTJk3Cq6++CgCIiorCxIkT8dprr2HPnj0AgOrqauzcuRN797b/GX5E1DyNRkByTikOXy7An5fzcTy1sN7lSaQOdugT7IHoEE/07+iJ3kHu8HXTziHUXofnIrydTXcdNLJ8DEM26p577sGFCxfqLLv1vm8JCQkNrmdnZ4fXXnsNr732Wr3XunXrhiNHjuieazQalJaW6vVeP/zwQ71lb7zxBhYtWoSnn34aXl5eSE5Ortfmxx9/rPM8Li4OgwYNwuDBgxvsDxG1v6ziKhz4Ow9/Xs7HkSsF9UZ+vJwliArxxIBQT0SHeiEy0B0SE9/VnKwbwxBZjHHjxuHSpUvIzMxEcHBwi9YRi8X4z3/+Y+TKiKgpGo2A0xnF+P1iLn5NzkVydmmd150k9hgU5oWhXeQY2kWOcD9X2HGeD7UjhiGyKC+++GKr2j/zzDNGqoSImqJSa3Docj52n83BbxdzkV+u0L1mJwL6dfTEsK5y3NFFjj7BHhDbc+SHTIdhiIiIDKJGrcHhKwX45Uw29l7IQXHl/67m7Cp1wJ3hPrg7whcjwn3hxTk+ZEYYhoiISG+CIOBMRgm+PZmOX85ko+iWACR3kWJcL3+M7umPAaFenPdDZothyABunQxMlof7j6j1CsoV2HkqE9+eyEDKjTLdcm9nCcZE+mN87wAMCvPmNX7IIjAMtUHtVZMrKyv1vjozmV7tlbDt7XkJfqKmCIKAQ5cLsOXodfyafAM1N698KHWww5hIfzwUFYSYTt5w4PwfsjAMQ21gb28PDw8P3T20nJycWnV5d41GA6VSierq6na/HUd7sIT+aTQa5OXlwcnJCQ4O/HMgakilsgbf/5WJTYev4XJuuW55nyB3TI4OxsQ+gXB35A1MyXLx07+Nau/QfutNRVtKEARUVVXB0dHRKu+RYyn9s7OzQ8eOHc26RiJTyC2tRtyfqfj6eBpKq2sAAM4SezwUFYRHB3VEhL+biSskMgyGoTYSiUQICAiAr68vVCpV8yvcQqVS4eDBg7jzzjvr3ajUGlhK/yQSidmOXBGZQmZxFT49cAXbEtOhrNHeMDnE2wnTY0IxOToIrjLz/Xsm0gfDkIHY29u3es6Jvb09ampqIJPJzDos6Mva+0dkbdIKKrF2/yV8/1embj5QVIgn5gzvjLsifHkhRLJaDENERDausEKJ//x+CVuOXodKrQ1BQ7t4Y97IrhjcyYuHkMnqMQwREdmoKqUanx9KxfqEKyhTaOcEDesqx/x7uiEqxNPE1RG1H4YhIiIbIwgCdp3NwVu/XEB2STUAoEeAG5aMi8Cwrj4mro6o/TEMERHZkKt55Vj603n8cSkfANDBwxH/GB2OSX0COSeIbBbDEBGRDVCpNVifcAX/+f0ylGoNJA52mDO8M+aM6AyZmBccJdvGMEREZOX+vlGGxTsv4GxmCQDgzm4+WDGpJ0LlziaujMg8MAwREVkpjUbAb5kiLDp+FCq1AHdHMZZN6oH7+nbgGWJEt2AYIiKyQvnlCszfdgp/ptkDEHBPd1+8c38v+LrJTF0akdlhGCIisjKHr+TjxW1JyCtTQGwnYPmknnh0UChHg4gawTBERGQlBEHAhj+uYuXui9AIQFdfZzwYUILJUUEMQkRN4A2ZiIisgKJGjUXfnsE7u7RBaHJUEHY8OxgBTqaujMj8cWSIiMjC5ZUp8OyXJ/BXWjHs7UR4Y3x3TB8SipqaGlOXRmQRGIaIiCxYWkElHo87hrTCSrjJHLDusf68ijRRKzEMERFZqOTsUjzx+XHklSkQ4u2EjTMGoJOPi6nLIrI4DENERBboxLVCPLUpEaXVNYjwd8UXMwfC15WnzRPpg2GIiMjCHE8txPTPj6NKpUZ0iCfiZgyAu6PY1GURWSyGISIiC3IqrQhPbtQGoWFd5fhsWjQcJby3GFFbMAwREVmI81klmP75cVQo1Yjp5I0NT0TzJqtEBsDrDBERWYDLueWYFnccpdU1iArxxP9NZxAiMhSGISIiM1dQrsCTm46jsEKJXh3csfHJAXCWcmCfyFAYhoiIzFi1So1nvjyJ9MIqdPRywuanBsJNxsnSRIbEMEREZKYEQcArO87g5PUiuMkc8PmMAfBylpi6LCKrwzBERGSmPvrtMn5MyoKDnQifPB6FLr68oCKRMTAMERGZof0puVj9698AgH/eF4mhXeQmrojIejEMERGZmcziKry0PQkA8Pjgjnh0YEfTFkRk5RiGiIjMiEqtwXNf/YXiShV6B7njjQk9TF0SkdWzqDB08OBBTJw4EYGBgRCJRPjhhx+aXefAgQOIioqCTCZDp06dsH79euMXSkSkpw9/vYSk9GK4O4qxbmp/SB14LSEiY7OoMFRRUYE+ffpg7dq1LWqfmpqKcePGYdiwYTh16hReffVVvPDCC9ixY4eRKyUiar0T1wrxccJlAMC7D/RCsJeTiSsisg0WddWusWPHYuzYsS1uv379enTs2BFr1qwBAHTv3h0nTpzA+++/jwcffNBIVRIRtV5ZtQovfZMEjQA82D8I43oFmLokIpthUWGotY4cOYLY2Ng6y0aPHo24uDioVCqIxfUvXKZQKKBQKHTPS0tLAQAqlQoqlcqg9dVuz9DbNRfsn+Wz9j6aU//e3XUB6YVVCPKQ4bWx3QxSkzn1z1isvY/sX9u33RIiQRAEg1fQDkQiEXbu3In77ruv0TbdunXDjBkz8Oqrr+qWHT58GEOHDkVWVhYCAur/z2vZsmVYvnx5veVbt26FkxOHrInI8K6UAh+d1/7fdF4PNbq6W+THMpFZqaysxNSpU1FSUgI3N7cm21r1yBCgDU23qs1+ty+vtWTJEixYsED3vLS0FMHBwYiNjW32h9laKpUK8fHxGDVqVIOjVJaO/bN81t5Hc+ifokaDD9cdAVCByVEd8OJ9PQ22bXPon7FZex/ZP/3VHtlpCasOQ/7+/sjJyamzLDc3Fw4ODvD29m5wHalUCqlUWm+5WCw22i+iMbdtDtg/y2ftfTRl/9Yd+BtX8ysgd5Hi9fE9jVKHte8/wPr7yP7pt82WsqizyVorJiYG8fHxdZbt27cP0dHRVv1LRUSWIb2wEp8kXAEALJvUA+5O/FwiMgWLCkPl5eVISkpCUlISAO2p80lJSUhLSwOgPcT1xBNP6NrPnj0b169fx4IFC5CcnIzPP/8ccXFxWLRokSnKJyKq451dyVDUaBDTyRvjefYYkclY1GGyEydOYOTIkbrntXN7pk+fjk2bNiE7O1sXjAAgLCwMu3btwksvvYR169YhMDAQH330EU+rJyKTO3wlH7vP5cBOBCyd1KPReYxEZHwWFYZGjBiBpk5+27RpU71lw4cPx19//WXEqoiIWketEbDi5wsAgMcHhyDC37AnZxBR61jUYTIiImvwY1ImLuaUwU3mgAWjupm6HCKbxzBERNSOlDUafBD/NwBgzogu8HCSmLgiImIYIiJqR18fT0NGURV8XaWYMSTU1OUQERiGiIjaTaWyBv/5/RIA4IW7u8JRwjvSE5kDhiEionay9Vga8suV6OjlhEcGBJu6HCK6iWGIiKgdVKvU+OzgVQDAcyM7Q2zPj18ic8G/RiKidvDdyQzklikQ6C7D/f2CTF0OEd2CYYiIyMhUag3WH9DeduOZOztB4sCPXiJzwr9IIiIj+/l0FjKKqiB3kWDKwI6mLoeIbsMwRERkRIIgIO7PVADAk0PDIBPzDDIic8MwRERkRInXinA+qxRSBztM5agQkVliGCIiMqKNh7SjQg/07wBPZ15tmsgcMQwRERlJRlEl9p7PAQDMGBJm4mqIqDEMQ0RERvLlkevQCMDQLt4I93c1dTlE1AiGISIiI1DUqPHNiXQAHBUiMncMQ0RERrDv/A0UVarg7ybDyHAfU5dDRE1gGCIiMoLtidpRoYejg+DAW28QmTX+hRIRGVhaQSX+vJwPkQiYHM0bshKZO4YhIiID234iDQBwRxc5gr2cTFwNETWHYYiIyIDUGgHfnsgAADzKiywSWQSGISIiAzp8JR+5ZQp4OolxT3c/U5dDRC3AMEREZEA7T2UCAMb3DuDd6YksBP9SiYgMpEqpxt5z2itO39e3g4mrIaKWYhgiIjKQX5NvoEKpRpCnI6JCPE1dDhG1EMMQEZGB/HDzENl9fTtAJBKZuBoiaimGISIiAyiqUOLA33kAgPv6BZq4GiJqDYYhIiID2Hs+BzUaAT0C3NDFlzdlJbIkDENERAaw57x24vS4Xv4mroSIWothiIiojUqqVDh0OR8AMCYywMTVEFFrMQwREbXR/ou5UKkFdPF1QRdfF1OXQ0StxDBERNRGu89lAwDGRvIQGZElYhgiImqDSmWN7iyy0T0ZhogsEcMQEVEbHEjJQ7VKg2AvR/QMdDN1OUSkB4YhIqI2iE++AQAY3cOfF1okslAMQ0REetJoBBxI0R4iu6u7r4mrISJ9MQwREenpdEYxCiqUcJU6YECol6nLISI9MQwREelp/8VcAMCwbnKI7flxSmSp+NdLRKSn31O0YWhkOA+REVkyhiEiIj3kllbjXGYpAGAEwxCRRWMYIiLSw/6bo0J9gtzh4yo1cTVE1BYMQ0REeth/UXsW2cgIjgoRWTqGISKiVqpRa3DoivbGrMO7+Zi4GiJqK4YhIqJWOptZgrLqGrjJHNA7yMPU5RBRGzEMERG10qHL2lGhIZ3lsLfjVaeJLB3DEBFRK/15MwwN7So3cSVEZAgMQ0RErVCprMHJ60UAgGFdGIaIrAHDEBFRKxxPLYRKLaCDhyNCvJ1MXQ4RGQDDEBFRK9TOF7qji5x3qSeyEhYXhj7++GOEhYVBJpMhKioKf/zxR6NtExISIBKJ6j0uXrzYjhUTkTX549LNMMT5QkRWw6LC0Pbt2zF//ny89tprOHXqFIYNG4axY8ciLS2tyfVSUlKQnZ2te3Tt2rWdKiYia1JYocTFnDIAwJDO3iauhogMxaLC0AcffICZM2di1qxZ6N69O9asWYPg4GB88sknTa7n6+sLf39/3cPe3r6dKiYia3I8tQAAEO7nCm8X3oKDyFo4mLqAllIqlTh58iQWL15cZ3lsbCwOHz7c5Lr9+vVDdXU1evTogddffx0jR45stK1CoYBCodA9Ly3V3ohRpVJBpVK1oQf11W7P0Ns1F+yf5bP2Pra2f0duXnU6OsTDIn4m1r7/AOvvI/vX9m23hEgQBMHgFRhBVlYWOnTogEOHDmHIkCG65e+88w42b96MlJSUeuukpKTg4MGDiIqKgkKhwJdffon169cjISEBd955Z4Pvs2zZMixfvrze8q1bt8LJiWeOENmyVaftkVkpwoyuavSTW8RHJ5HNqqysxNSpU1FSUgI3N7cm21rMyFCt28/eEASh0TM6wsPDER4ernseExOD9PR0vP/++42GoSVLlmDBggW656WlpQgODkZsbGyzP8zWUqlUiI+Px6hRoyAWiw26bXPA/lk+a+9ja/pXUqVC1tH9AIBn7r/LIu5Ub+37D7D+PrJ/+qs9stMSFhOG5HI57O3tkZOTU2d5bm4u/Pz8WrydwYMHY8uWLY2+LpVKIZXW/5ATi8VG+0U05rbNAftn+ay9jy3p3+nLhRAEoJPcGYFeLu1UmWFY+/4DrL+P7J9+22wpi5lALZFIEBUVhfj4+DrL4+Pj6xw2a86pU6cQEBBg6PKIyModSy0EAAzq5GXiSojI0CxmZAgAFixYgGnTpiE6OhoxMTH47LPPkJaWhtmzZwPQHuLKzMzEF198AQBYs2YNQkND0bNnTyiVSmzZsgU7duzAjh07TNkNIrJAx65qzyQbGMYwRGRtLCoMPfLIIygoKMCKFSuQnZ2NyMhI7Nq1CyEhIQCA7OzsOtccUiqVWLRoETIzM+Ho6IiePXvil19+wbhx40zVBSKyQOWKGpzL0s4/GBTG6wsRWRuLCkMAMHfuXMydO7fB1zZt2lTn+csvv4yXX365HaoiImv21/UiqDUCgjwdEejhaOpyiMjALGbOEBGRqdTepX5gKA+REVkjhiEiomb8laYNQ/1DPE1cCREZA8MQEVET1BoBp9KKAQBRDENEVolhiIioCX/fKEO5ogYuUgd083M1dTlEZAQMQ0RETThxc75Qv44esLdr+Gr3RGTZGIaIiJrw180w1L8jD5ERWSuGISKiJtSeScb5QkTWi2GIiKgRuWXVSCushEgE9O3oYepyiMhIGIaIiBrx1/ViAEC4nyvcZNZ7k0wiW8cwRETUiFNptZOneYiMyJoxDBERNSIpvRiA9kwyIrJeDENERA1QawScyywBAPQJ8jBtMURkVAxDREQNuJJXjgqlGk4Se3TxdTF1OURkRAxDREQNOH3zEFlkB3debJHIyjEMERE14HRGMQCgb7CHSesgIuNjGCIiasCZDO18od5B7iauhIiMjWGIiOg2iho1krNLAXDyNJEtYBgiIrpNcnYZVGoB3s4SBHk6mrocIjIyhiEiotvUTp7uHeQOkYiTp4msHcMQEdFtaidP9+HkaSKbwDBERHSb2pEhzhcisg0MQ0REtyitVuFqfgUAnklGZCsYhoiIbnEuowSCAAR5OsLbRWrqcoioHTjos9K1a9fwxx9/4Nq1a6isrISPjw/69euHmJgYyGQyQ9dIRNRuTt+8vhDnCxHZjlaFoa1bt+Kjjz7C8ePH4evriw4dOsDR0RGFhYW4cuUKZDIZHnvsMbzyyisICQkxVs1EREbzv/lCPERGZCtaHIb69+8POzs7zJgxA9988w06duxY53WFQoEjR45g27ZtiI6Oxscff4zJkycbvGAiImM6U3smGSdPE9mMFoehf/7znxg/fnyjr0ulUowYMQIjRozAW2+9hdTUVIMUSETUXgrKFcgqqYZIBPTswJEhIlvR4jDUVBC6nVwuh1wu16sgIiJTOZ+lvQVHmNwZLlK9plQSkQXS62yyuLi4BpfX1NRgyZIlbSqIiMhUzmVpJ09HBnJUiMiW6BWGFi5ciAcffBCFhYW6ZRcvXsTAgQPxzTffGKw4IqL2dD5TOzLUM9DNxJUQUXvSKwydOnUKN27cQK9evRAfH49169ahf//+iIyMRFJSkoFLJCJqH7qRIc4XIrIpeh0UDwsLw8GDB/HSSy9hzJgxsLe3xxdffIEpU6YYuj4ionZRWq3C9YJKABwZIrI1el+B+r///S++/vprDBkyBB4eHtiwYQOysrIMWRsRUbu5cHPydJCnIzycJCauhojak15h6Nlnn8XDDz+Ml19+GQcPHsSZM2cglUrRq1cvzhkiIot0LlN7iIyjQkS2R6/DZIcOHcKxY8fQp08fAIC/vz927dqFdevW4amnnsLDDz9s0CKJiIyt9rR6nklGZHv0CkMnT56EVFr/BobPPfcc7rnnnjYXRUTU3mpHhjh5msj26HWYrKEgVCs8PFzvYoiITKFKqcaVvHIAQM8OPExGZGtaHIbGjBmDw4cPN9uurKwM7733HtatW9emwoiI2svFG2XQCICvqxS+rjJTl0NE7azFh8kmT56Mhx9+GK6urpg0aRKio6MRGBgImUyGoqIiXLhwAX/++Sd27dqFCRMm4F//+pcx6yYiMpjaM8k4eZrINrU4DM2cORPTpk3Dd999h+3bt2PDhg0oLi4GAIhEIvTo0QOjR4/GyZMneaiMiCzK+ewyAJwvRGSrWjWBWiKRYOrUqZg6dSoAoKSkBFVVVfD29oZYLDZKgURExnZeNzLEMERki9p0W2Z3d3e4u/PDg4gsV40GuJSrnTwdycnTRDZJ7zD0999/IyEhAbm5udBoNHVee/PNN9tcGBFRe8ipAlRqAR5OYnTwcDR1OURkAnqFoQ0bNmDOnDmQy+Xw9/eHSCTSvSYSiRiGiMhipJdrP796BrrV+SwjItuhVxh666238Pbbb+OVV14xdD1ERO0qo0IbgHjlaSLbpddFF4uKijB58mRD10JE1O5qw1BPnklGZLP0CkOTJ0/Gvn37DF0LEVG7UmsEZFZqv4/kNYaIbJZeh8m6dOmCN954A0ePHkWvXr3qnVb/wgsvGKQ4IiJjuppfAZVGBGeJPUK9nU1dDhGZiF4jQ5999hlcXFxw4MABrF27FqtXr9Y91qxZY+AS6/r4448RFhYGmUyGqKgo/PHHH022P3DgAKKioiCTydCpUyesX7/eqPURkeWovfJ09wBX2Nlx8jSRrdJrZCg1NdXQdbTI9u3bMX/+fHz88ccYOnQoPv30U4wdOxYXLlxAx44d67VPTU3FuHHj8PTTT2PLli04dOgQ5s6dCx8fHzz44IMm6AERmZPaK0/3COAhMiJbptfIkKl88MEHmDlzJmbNmoXu3btjzZo1CA4OxieffNJg+/Xr16Njx45Ys2YNunfvjlmzZuGpp57C+++/386VE5E5+t+Vp11NXAkRmZLeF13MyMjATz/9hLS0NCiVyjqvffDBB20u7HZKpRInT57E4sWL6yyPjY3F4cOHG1znyJEjiI2NrbNs9OjRiIuLg0qlavAWIgqFAgqFQve8tFT7YalSqaBSqdrajTpqt2fo7ZoL9s/yWXMfNRoBF7K1f9/hPk5W2Udr3n+1rL2P7F/bt90SeoWh3377DZMmTUJYWBhSUlIQGRmJa9euQRAE9O/fX59NNis/Px9qtRp+fn51lvv5+SEnJ6fBdXJychpsX1NTg/z8fAQEBNRb591338Xy5cvrLd+3bx+cnJza0IPGxcfHG2W75oL9s3zW2Mf8aqBc4QAHkYCrSUdw/YypKzIea9x/t7P2PrJ/rVdZWdnitnqFoSVLlmDhwoVYsWIFXF1dsWPHDvj6+uKxxx7DmDFj9Nlki91+hVhBEJq8amxD7RtaXmvJkiVYsGCB7nlpaSmCg4MRGxsLNzfDzitQqVSIj4/HqFGjrPJGt+yf5bPmPu4+lwOcOoNAJ2DMaOvrH2Dd+6+WtfeR/dNf7ZGdltArDCUnJ+Prr7/WbsDBAVVVVXBxccGKFStw7733Ys6cOfpstklyuRz29vb1RoFyc3Prjf7U8vf3b7C9g4MDvL29G1xHKpVCKpXWWy4Wi432i2jMbZsD9s/yWWMfk29UAACCXASr7N+trL1/gPX3kf3Tb5stpdcEamdnZ928msDAQFy5ckX3Wn5+vj6bbJZEIkFUVFS9obT4+HgMGTKkwXViYmLqtd+3bx+io6Ot+peKiJp3LrMEABDkLJi4EiIyNb1GhgYPHoxDhw6hR48eGD9+PBYuXIizZ8/i+++/x+DBgw1do86CBQswbdo0REdHIyYmBp999hnS0tIwe/ZsANpDXJmZmfjiiy8AALNnz8batWuxYMECPP300zhy5Aji4uJ0o1pEZJsEQdCdSRbMMERk8/QKQx988AHKy8sBAMuWLUN5eTm2b9+OLl26YPXq1QYt8FaPPPIICgoKsGLFCmRnZyMyMhK7du1CSEgIACA7OxtpaWm69mFhYdi1axdeeuklrFu3DoGBgfjoo494jSEiG5ddUo3CCiUc7EQIMM55EURkQfQKQ506ddJ97+TkhI8//thgBTVn7ty5mDt3boOvbdq0qd6y4cOH46+//jJyVURkSWoPkXXxdYHYrsjE1RCRqek1Z6hTp04oKCiot7y4uLhOUCIiMkfneLFFIrqFXmHo2rVrUKvV9ZYrFApkZma2uSgiImM6f3NkqCdvw0FEaOVhsp9++kn3/d69e+Hu7q57rlar8dtvvyE0NNRgxRERGcO5rJthKNANOYUmLoaITK5VYei+++4DoL1g4fTp0+u8JhaLERoain//+98GK46IyNByy6pxo1QBkQiI8HdBzjlTV0REptaqMKTRaABoz9JKTEyEXC43SlFERMZSe0p9Zx8XOEn0vj0jEVkRvT4JUlNTDV0HEVG7qJ0vFBnI+UJEpKXXBOoXXngBH330Ub3la9euxfz589taExGR0ZzL1I4MRXZwb6YlEdkKvcLQjh07MHTo0HrLhwwZgu+++67NRRERGUvt5OkeHBkiopv0CkMFBQV1ziSr5ebmZrR7kxERtVVxpRIZRVUAgJ6BHBkiIi29wlCXLl2wZ8+eest3797Niy4SkdmqnTzd0csJ7o68WTMRaek1gXrBggWYN28e8vLycNdddwEAfvvtN/z73//GmjVrDFkfEZHB1N6GI7IDD5ER0f/oFYaeeuopKBQKvP322/jnP/8JAAgNDcUnn3yCJ554wqAFEhEZyv9uw8FDZET0P60OQzU1Nfjqq69w//33Y86cOcjLy4OjoyNcXFyMUR8RkcHoTqvnmWREdItWzxlycHDAnDlzoFAoAAA+Pj4MQkRk9sqqVbiaXwFAexsOIqJaek2gHjRoEE6dOmXoWoiIjCY5uwwAEOAug9xFauJqiMic6DVnaO7cuVi4cCEyMjIQFRUFZ2fnOq/37t3bIMURERlK7eRpzhciotvpFYYeeeQRANorUd9OJBJBrVa3rSoiIgOrvdgizyQjotvx3mREZBPO196GgyNDRHQbvcJQSEgIAODChQtIS0uDUqnUvSYSiXSvExGZg2qVGpfzygHwTDIiqk+vMHT16lXcf//9OHv2LEQiEQRBAKANQgB4mIyIzMr5rFKoNQLkLhL4uXHyNBHVpdfZZC+++CLCwsJw48YNODk54dy5czh48CCio6ORkJBg4BKJiNrmdHoxAKBPkIfuP21ERLX0Ghk6cuQIfv/9d/j4+MDOzg729va444478O677+KFF17gafdEZFbOZBQDAPoEe5i0DiIyT3qNDKnVat2FFuVyObKysgBo5xKlpKQYrjoiIgM4naE9k6x3EOcLEVF9eo0MRUZG4syZM+jUqRMGDRqEVatWQSKR4LPPPuNd64nIrJRUqpB688rTfYI8TFsMEZklvcLQ66+/jooK7YfLW2+9hQkTJmDYsGHw9vbG9u3bDVogEVFbnMksBgCEeDvB01li2mKIyCzpFYZGjx6t+75Tp064cOECCgsL4enpycmJRGRWaidP9+aoEBE1Qq8w1BAvLy9DbYqIyGBq5wv14XwhImqEXhOoiYgshe60ep5JRkSNYBgiIquVU1KN3DIF7O1E6BnIe5IRUcMYhojIaiXdHBXq5ucKJ4nBZgUQkZVhGCIiq6W72CLnCxFRExiGiMhqneaVp4moBRiGiMgqaTQCzqTzytNE1DyGISKySqkFFShT1EAmtkM3P1dTl0NEZoxhiIisUu0p9T0D3SG250cdETWOnxBEZJVqzyTj/ciIqDkMQ0RklU5eLwIARIV4mrgSIjJ3DENEZHUqFDVIzi4FwDBERM1jGCIiq3M6vRgaAejg4Qh/d5mpyyEiM8cwRERWh4fIiKg1GIaIyOqcTGMYIqKWYxgiIqui0Qj4iyNDRNQKDENEZFWu5JWjtLoGjmJ7RPjzYotE1DyGISKyKrXzhfoGe8CBF1skohbgJwURWRVOniai1mIYIiKrknitEADDEBG1HMMQEVmNG6XVuFZQCTsREBXKMERELWMxYaioqAjTpk2Du7s73N3dMW3aNBQXFze5zowZMyASieo8Bg8e3D4FE1G7O5aqHRXqEegGN5nYxNUQkaVwMHUBLTV16lRkZGRgz549AIBnnnkG06ZNw88//9zkemPGjMHGjRt1zyUSiVHrJCLTOXa1AAAwKMzbxJUQkSWxiDCUnJyMPXv24OjRoxg0aBAAYMOGDYiJiUFKSgrCw8MbXVcqlcLf37+9SiUiE6odGRoY5mXiSojIkljEYbIjR47A3d1dF4QAYPDgwXB3d8fhw4ebXDchIQG+vr7o1q0bnn76aeTm5hq7XCIygfxyBS7nlgMABoYyDBFRy1nEyFBOTg58fX3rLff19UVOTk6j640dOxaTJ09GSEgIUlNT8cYbb+Cuu+7CyZMnIZVKG1xHoVBAoVDonpeWau98rVKpoFKp2tiTumq3Z+jtmgv2z/JZUh+PXM4DAIT7ucBFImpRzZbUP31Ye/8A6+8j+9f2bbeESBAEweAVtNCyZcuwfPnyJtskJiZi37592Lx5M1JSUuq81rVrV8ycOROLFy9u0ftlZ2cjJCQE27ZtwwMPPNCqmrZu3QonJ6cWvQ8Rtb8dqXY4mGOHYX4aPNRJY+pyiMjEKisrMXXqVJSUlMDNza3JtiYdGZo3bx6mTJnSZJvQ0FCcOXMGN27cqPdaXl4e/Pz8Wvx+AQEBCAkJwaVLlxpts2TJEixYsED3vLS0FMHBwYiNjW32h9laKpUK8fHxGDVqFMRi6zvzhf2zfJbUx0/WHQFQhskj+mJsZMvmCVpS//Rh7f0DrL+P7J/+ao/stIRJw5BcLodcLm+2XUxMDEpKSnD8+HEMHDgQAHDs2DGUlJRgyJAhLX6/goICpKenIyAgoNE2Uqm0wUNoYrHYaL+Ixty2OWD/LJ+597GoQomUG2UAgJguvq2u1dz711bW3j/A+vvI/um3zZayiAnU3bt3x5gxY/D000/j6NGjOHr0KJ5++mlMmDChzplkERER2LlzJwCgvLwcixYtwpEjR3Dt2jUkJCRg4sSJkMvluP/++03VFSIygsNXCiAIQLifK3xcG54PSETUGIsIQwDw1VdfoVevXoiNjUVsbCx69+6NL7/8sk6blJQUlJSUAADs7e1x9uxZ3HvvvejWrRumT5+Obt264ciRI3B15Z2siazJn5fzAQBDuzQ/0kxEdDuLOJsMALy8vLBly5Ym29w6F9zR0RF79+41dllEZAYO3QxDw7oyDBFR61nMyBARUUPSCiqRVlgJBzsRL7ZIRHphGCIii1Z7iKx/R084Sy1msJuIzAjDEBFZtNpDZHfwEBkR6YlhiIgslkYj4NAVTp4morZhGCIii3U+qxTFlSq4SB3QJ8jd1OUQkYViGCIii7U/RXvj5SGdveFgz48zItIPPz2IyGL9flEbhu6KqH8jZyKilmIYIiKLVFCuwOmMYgDASIYhImoDhiEiskgJKXkQBKBnoBv83GSmLoeILBjDEBFZpN9TeIiMiAyDYYiILI5KrcHBv/MA8BAZEbUdwxARWZyT14tQVl0DL2cJ+gR5mLocIrJwDENEZHF+S74BABjezQf2diITV0NElo5hiIgsiiAI2HM+BwAQ28PPxNUQkTVgGCIii3IhuxTphVWQie0wPNzH1OUQkRVgGCIii7LnnHZUaHg3HzhJeJd6Imo7hiEisii7b4ahMZH+Jq6EiKwFwxARWYzLuWW4nFsOsb0Id0VwvhARGQbDEBFZjNpDZEO7yOHuKDZxNURkLRiGiMhi7Dp78xBZTx4iIyLDYRgiIovw940yXMguhYOdCKMZhojIgBiGiMgi/HAqEwAwItwXns4SE1dDRNaEYYiIzJ5GI+DHpCwAwH39Ak1cDRFZG4YhIjJ7J9OKkFlcBRepA+7pzrPIiMiwGIaIyOzVHiIb3dMfMrG9iashImvDMEREZk1Ro8YvZ7MBAPf362DiaojIGjEMEZFZi79wA8WVKvi5SRHT2dvU5RCRFWIYIiKztu14OgDg4ehg2NuJTFwNEVkjhiEiMltpBZX483I+RCJtGCIiMgaGISIyW9+c0I4K3dFFjmAvJxNXQ0TWimGIiMxSjVqDb09qw9CjAzuauBoismYMQ0Rkln67mIsbpQp4O0t4bSEiMiqGISIySxsPpQIAHhkQDIkDP6qIyHj4CUNEZud8VgmOXi2EvZ0I02JCTF0OEVk5hiEiMjubDl0DAIyN9EeAu6NpiyEiq8cwRERmJb9cobsp61N3hJm4GiKyBQxDRGRWvjqaBqVagz7BHujf0dPU5RCRDWAYIiKzUaGowcbD2onTMzkqRETthGGIiMzG1mNpKK5UIUzujPG9AkxdDhHZCIYhIjIL1So1PvvjKgBgzvDOvA8ZEbUbhiEiMgvfnsxAXpkCge4y3Nevg6nLISIbwjBERCZXrVJjfcIVAMCzwzvzIotE1K74iUNEJvfVsTRkFlchwF2GRwbw7vRE1L4YhojIpMoVNVi3/zIA4MW7u0ImtjdxRURkaxiGiMik/u+PqyisUKKT3BkPRQWZuhwiskEMQ0RkMrll1dhwUHsG2aLR4XCw50cSEbU/fvIQkcn8a08KKpRq9Alyx9hIf1OXQ0Q2imGIiEzidHoxvj2ZAQBYOqknRCJeV4iITMNiwtDbb7+NIUOGwMnJCR4eHi1aRxAELFu2DIGBgXB0dMSIESNw/vx54xZKRM3SaAQs+1n7t/hAvw68BxkRmZTFhCGlUonJkydjzpw5LV5n1apV+OCDD7B27VokJibC398fo0aNQllZmRErJaLmfHcyA6fSiuEssccrYyNMXQ4R2TiLCUPLly/HSy+9hF69erWovSAIWLNmDV577TU88MADiIyMxObNm1FZWYmtW7cauVoiakxemQJv70oGALx4T1f4uclMXBER2TqLCUOtlZqaipycHMTGxuqWSaVSDB8+HIcPHzZhZUS2bfnP51FSpULPQDc8NZR3pici03MwdQHGkpOTAwDw8/Ors9zPzw/Xr19vdD2FQgGFQqF7XlpaCgBQqVRQqVQGrbF2e4berrlg/yyfofv428Vc/PdMNuztRHj73h4QNGqoNGqDbFsf1r4Prb1/gPX3kf1r+7ZbwqRhaNmyZVi+fHmTbRITExEdHa33e9x+hoogCE2etfLuu+82WNO+ffvg5OSkdx1NiY+PN8p2zQX7Z/kM0cdyFbDytD0AEYb7qXE96U9cT2rzZg3C2vehtfcPsP4+sn+tV1lZ2eK2Jg1D8+bNw5QpU5psExoaqte2/f211yzJyclBQECAbnlubm690aJbLVmyBAsWLNA9Ly0tRXBwMGJjY+Hm5qZXLY1RqVSIj4/HqFGjIBaLDbptc8D+WT5D9VEQBDz39WmUqXLRxccZHz492Cxuu2Ht+9Da+wdYfx/ZP/3VHtlpCZOGIblcDrlcbpRth4WFwd/fH/Hx8ejXrx8A7RlpBw4cwHvvvdfoelKpFFKptN5ysVhstF9EY27bHLB/lq+tffwmMR3xybkQ24vw4aP94OpkXpOmrX0fWnv/AOvvI/un3zZbymImUKelpSEpKQlpaWlQq9VISkpCUlISysvLdW0iIiKwc+dOANrDY/Pnz8c777yDnTt34ty5c5gxYwacnJwwdepUU3WDyOb8faMMS3/SXlNowahw9Ax0N3FFRER1WcwE6jfffBObN2/WPa8d7dm/fz9GjBgBAEhJSUFJSYmuzcsvv4yqqirMnTsXRUVFGDRoEPbt2wdXV9d2rZ3IVlUoajBny0lUqdQY2sUbz9zZydQlERHVYzFhaNOmTdi0aVOTbQRBqPNcJBJh2bJlWLZsmfEKI6IGCYKAJd+fxZW8Cvi7yfDhlH6wt+MtN4jI/FjMYTIisiyfHryKn05nwcFOhLVT+0HuUn8uHhGROWAYIiKDi79wA+/tuQgAeGNCD0SHepm4IiKixjEMEZFBnc8qwfxtpyAIwGODOuKJmBBTl0RE1CSGISIymGv5FZj+eSIqlGrEdPLGskk9m7zIKRGROWAYIiKDuFFajcfjjiG/XIHuAW5YPy0KYnt+xBCR+eMnFRG1WXGlEk/EHUdGURVCvZ3wxVMD4e5ovReIIyLrwjBERG1SXKnE9M+PI+VGGXxdpfhy5iD4uPLMMSKyHBZznSEiMj/55Qo8/n/HcDGnDJ5OYnw5cxCCvYxzQ2MiImNhGCIivdworcbUDUdxJa8Cchcptj49CN38eHV3IrI8DENE1Gqp+RWYsfE4rhdUIsBdhq9mDUInHxdTl0VEpBeGISJqleOphXjmyxMorlQh2MsRW2cN5qExIrJoDENE1GI7T2Xgle/OQqnWoE+QOzZMj4avq8zUZRERtQnDEBE1q0atwerfLuLjhCsAgDE9/bH6kb5wlNibuDIiorZjGCKiJpUqgSc3n8TR1CIAwLN3dsIrYyJgxzvQE5GVYBgiokYlXivCv87Yo1RVBCeJPVY+2BuT+gSauiwiIoNiGCKiepQ1Gqz59W+sP3AFGkGEzj7O+HRaFLr48tR5IrI+DENEVMffN8owf1sSLmSXAgAG+Giw4dlB8HBxNHFlRETGwTBERAC0o0GfHbyCj36/DGWNBp5OYqyY1AOa6yfhLOVHBRFZL37CERESrxViyfdncTm3HAAwMtwH7z3UG54ye+y6buLiiIiMjGGIyIbdKK3G+3tT8O3JDACA3EWCNyb0wKQ+gRCJRFCpVCaukIjI+BiGiGxQpbIGnx28ik8PXEWVSg0AeHRgMF4ZEwEPJ4mJqyMial8MQ0Q2pEatwc5TmXh/XwpulCoAAFEhnnh9fHf06+hp4uqIiEyDYYjIBtSoNfgxKQtr919Gan4FACDYyxFLxnbH2Eh/iES8gCIR2S6GISIrVjsStG7/ZVwrqAQAeDqJMWdEZ0wfEgqpA2+nQUTEMERkhUqqVNiemIbNh68js7gKAODlLMEzd3bCtMEhPFWeiOgW/EQksiJpBZXYeDgV3ySmo0KpnRjtfTMEPc4QRETUIH4yElk4lVqD35Jz8fXxNBy8lAdB0C7v6uuCWcPCcG/fDpCJeTiMiKgxDENEFio1vwLfnkjHtyczkFem0C2/s5sPZt0RhmFd5ZwYTUTUAgxDRBYkt6wa/z2djR+TMnE6o0S3XO4iweToYEwZEIwQb2cTVkhEZHkYhojMXEmlCvHJN/BjUiYOXc6H5uZhMDsRcEdXHzw6IBh3d/eDxMHOtIUSEVkohiEiM5RVXIX4Czew70IOjl0tRE1tAgLQN9gD9/UNxPjegfBxlZqwSiIi68AwRGQG1BoBZzNLcPDvPPyafANnbjkEBgDd/FwwoXcg7u0byMNgREQGxjBEZCLZJVU4+HceDl7Kx6HL+Siu/N9NUUUiIDrEE7E9/DGqhx9C5QxARETGwjBE1E7yyhRIvFaI46mFOHQ5H5dyy+u87ipzwNDOcgwP98E93f14CIyIqJ0wDBEZSVZxFY6nFuJYaiGOpRbgal5FndftREDvIA/c2c0Hd3aVo2+wBxzsOQmaiKi9MQwRGUBZtQpnM0qQlFGM0+nFOJ1egpzS6nrtIvxdMTDMC4PCvDG0izc8nCQmqJaIiG7FMETUShWKGlzMKcPZjCLsumyHjz46hKv5FborP9eytxMhsoM7BoV5YWCoF6JDPRl+iIjMEMMQUSMEQUBmcRWSs8uQnF2qe1wvrLwl+NgB0B7+6uDhiL7BHugb7IE+wR6I7OAGJwn/xIiIzB0/qcnmCYKAnNJqXM4tx5XcclzOK8elG+VIzi5FaXVNg+v4uEoR4ecCx6o8PDgyCv1DvDnhmYjIQjEMkc1Q1KiRXlipDT15FTe/agNQ7R3eb+dgJ0IXXxd0D3BD9wDXm1/dIHeRQqVSYdeuXbgr3Adisbide0NERIbCMERWQxAElFSpcL2gEtcLK5FeWInrBRVIK6xEWkElskur683rqeVgJ0KItxM6+7igs68Luvi4ICLAFV18XSB14B3fiYisGcMQWQxBEFBUqUJWcRWyiquQXVKNrOIqpBdVIq2wEtcLKlHWyGGtWi5SB3T2cUZnXxdt8PFxQRdfF4R4O0HM09qJiGwSwxCZBUEQUFpdg7yyamQVa0NOVkk1sourkFVSheziamSVVKFapWl2W35uUnT0ckJHL2eEeDtpv7/51dtZApFI1A49IiIiS8EwREalEYCCCiWKqqqQW6ZAbmk1cssUyCtTILesGrmlCu3ysuoWBR0AkLtI0cFDhgB3RwR4yBDk6YSQm4En2NMJjhIe1iIiopZjGKJWEQQBFUo1CsuVyK9QoLBcicIKJQoqlCisUNz8qn1og489NEcTWrx9V5kDAm+GnEAPRwS6a78GuDuig4cj/NylnMNDREQGxTBkwzQaAWXVNSiuUqKkSoXiShWKq1QoqVKhpFKJwgpVvYBTUKGEsqZlIzha2kNS3s4S+LhK4esmg6+r9H8P3XMZfFylHNUhIqJ2xzBk4VRqDcqra1BWXYMyhQpl1TUordKGmtKbAafk5vPiSqXuteJKFUqrVY2eXdUcmdgO3s5SeLtI4OWsfXg7S+DlLIW3swTeLhK4y+xxPvEQJk8aAycZr8FDRETmiWHIRARBQIWiBiVK4HJuOarU+F+oqVahXFGD0uqam8u0IadccfN7xf/atXSeTVMcxfbwcBLD3VH78HASw8NRAg8nsTbkuEhvBp2bocdF0qIrK6tUKmSeAc/SIiIis2YxYejtt9/GL7/8gqSkJEgkEhQXFze7zowZM7B58+Y6ywYNGoSjR48aqcqWW/PrJXz42yUADsDJw23enkxsB1eZGK5SB7g6iuFxM9S43/ze3Umi+14XfG5+5RwcIiKyZRYThpRKJSZPnoyYmBjExcW1eL0xY8Zg48aNuucSiXncKNNVpv3RiyDAzVEMF6kYrjIHuMnEcJE5wFXmABepgzbg3HyuXXbL85vfu8gcOPpCRESkJ4sJQ8uXLwcAbNq0qVXrSaVS+Pv7G6GitnlsUAge6heAhF/3Yfz40bydAxERkYlYTBjSV0JCAnx9feHh4YHhw4fj7bffhq+vb6PtFQoFFAqF7nlpaSkA7fwXlUplsLocRIBgJ0AkgkG3a05q+8X+WS5r7yP7Z/msvY/sX9u33RIiQdD3fCLT2LRpE+bPn9+iOUPbt2+Hi4sLQkJCkJqaijfeeAM1NTU4efIkpNKGz25atmyZbhTqVlu3boWTk1NbyyciIqJ2UFlZialTp6KkpARubm5NtjVpGGoseNwqMTER0dHRuuetCUO3y87ORkhICLZt24YHHnigwTYNjQwFBwcjPz+/2R9ma6lUKsTHx2PUqFFWeZiM/bN81t5H9s/yWXsf2T/9lZaWQi6XtygMmfQw2bx58zBlypQm24SGhhrs/QICAhASEoJLly412kYqlTY4aiQWi432i2jMbZsD9s/yWXsf2T/LZ+19ZP/022ZLmTQMyeVyyOXydnu/goICpKenIyAgoN3ek4iIiMybxZyPnZaWhqSkJKSlpUGtViMpKQlJSUkoLy/XtYmIiMDOnTsBAOXl5Vi0aBGOHDmCa9euISEhARMnToRcLsf9999vqm4QERGRmbGYs8nefPPNOhdQ7NevHwBg//79GDFiBAAgJSUFJSUlAAB7e3ucPXsWX3zxBYqLixEQEICRI0di+/btcHV1bff6iYiIyDxZTBjatGlTs9cYunUuuKOjI/bu3WvkqoiIiMjSWcxhMiIiIiJjsJiRIVOpHW2qvfiiIalUKlRWVqK0tNQqzxJg/yyftfeR/bN81t5H9k9/tf9ut+QKQgxDzSgrKwMABAcHm7gSIiIiaq2ysjK4u7s32cbirkDd3jQaDbKysuDq6gqRSGTQbdde0DE9Pd3gF3Q0B+yf5bP2PrJ/ls/a+8j+6U8QBJSVlSEwMBB2dk3PCuLIUDPs7OwQFBRk1Pdwc3Ozyl/yWuyf5bP2PrJ/ls/a+8j+6ae5EaFanEBNRERENo1hiIiIiGwaw5AJSaVSLF26tMF7oVkD9s/yWXsf2T/LZ+19ZP/aBydQExERkU3jyBARERHZNIYhIiIismkMQ0RERGTTGIaIiIjIpjEMGdHbb7+NIUOGwMnJCR4eHg22SUtLw8SJE+Hs7Ay5XI4XXngBSqWyye0qFAo8//zzkMvlcHZ2xqRJk5CRkWGEHrROQkICRCJRg4/ExMRG15sxY0a99oMHD27HylsuNDS0Xq2LFy9uch1BELBs2TIEBgbC0dERI0aMwPnz59up4pa7du0aZs6cibCwMDg6OqJz585YunRps7+P5r7/Pv74Y4SFhUEmkyEqKgp//PFHk+0PHDiAqKgoyGQydOrUCevXr2+nSlvn3XffxYABA+Dq6gpfX1/cd999SElJaXKdxv5GL1682E5Vt86yZcvq1erv79/kOpay/4CGP09EIhGee+65Bttbwv47ePAgJk6ciMDAQIhEIvzwww91Xtf383DHjh3o0aMHpFIpevTogZ07dxq0boYhI1IqlZg8eTLmzJnT4OtqtRrjx49HRUUF/vzzT2zbtg07duzAwoULm9zu/PnzsXPnTmzbtg1//vknysvLMWHCBKjVamN0o8WGDBmC7OzsOo9Zs2YhNDQU0dHRTa47ZsyYOuvt2rWrnapuvRUrVtSp9fXXX2+y/apVq/DBBx9g7dq1SExMhL+/P0aNGqW77525uHjxIjQaDT799FOcP38eq1evxvr16/Hqq682u6657r/t27dj/vz5eO2113Dq1CkMGzYMY8eORVpaWoPtU1NTMW7cOAwbNgynTp3Cq6++ihdeeAE7duxo58qbd+DAATz33HM4evQo4uPjUVNTg9jYWFRUVDS7bkpKSp391bVr13aoWD89e/asU+vZs2cbbWtJ+w8AEhMT6/QtPj4eADB58uQm1zPn/VdRUYE+ffpg7dq1Db6uz+fhkSNH8Mgjj2DatGk4ffo0pk2bhocffhjHjh0zXOECGd3GjRsFd3f3est37dol2NnZCZmZmbplX3/9tSCVSoWSkpIGt1VcXCyIxWJh27ZtumWZmZmCnZ2dsGfPHoPX3hZKpVLw9fUVVqxY0WS76dOnC/fee2/7FNVGISEhwurVq1vcXqPRCP7+/sLKlSt1y6qrqwV3d3dh/fr1RqjQsFatWiWEhYU12cac99/AgQOF2bNn11kWEREhLF68uMH2L7/8shAREVFn2bPPPisMHjzYaDUaSm5urgBAOHDgQKNt9u/fLwAQioqK2q+wNli6dKnQp0+fFre35P0nCILw4osvCp07dxY0Gk2Dr1va/gMg7Ny5U/dc38/Dhx9+WBgzZkydZaNHjxamTJlisFo5MmRCR44cQWRkJAIDA3XLRo8eDYVCgZMnTza4zsmTJ6FSqRAbG6tbFhgYiMjISBw+fNjoNbfGTz/9hPz8fMyYMaPZtgkJCfD19UW3bt3w9NNPIzc31/gF6um9996Dt7c3+vbti7fffrvJw0ipqanIycmps7+kUimGDx9udvurISUlJfDy8mq2nTnuP6VSiZMnT9b52QNAbGxsoz/7I0eO1Gs/evRonDhxAiqVymi1GkJJSQkAtGh/9evXDwEBAbj77ruxf/9+Y5fWJpcuXUJgYCDCwsIwZcoUXL16tdG2lrz/lEoltmzZgqeeeqrZm4Jb0v67lb6fh43tV0N+hjIMmVBOTg78/PzqLPP09IREIkFOTk6j60gkEnh6etZZ7ufn1+g6phIXF4fRo0cjODi4yXZjx47FV199hd9//x3//ve/kZiYiLvuugsKhaKdKm25F198Edu2bcP+/fsxb948rFmzBnPnzm20fe0+uX0/m+P+ut2VK1fwn//8B7Nnz26ynbnuv/z8fKjV6lb97Bv6m/Tz80NNTQ3y8/ONVmtbCYKABQsW4I477kBkZGSj7QICAvDZZ59hx44d+P777xEeHo67774bBw8ebMdqW27QoEH44osvsHfvXmzYsAE5OTkYMmQICgoKGmxvqfsPAH744QcUFxc3+Z9HS9t/t9P387Cx/WrIz1Detb6Vli1bhuXLlzfZJjExsdk5MrUa+h+AIAjN/s/AEOu0lD59zsjIwN69e/HNN980u/1HHnlE931kZCSio6MREhKCX375BQ888ID+hbdQa/r30ksv6Zb17t0bnp6eeOihh3SjRY25fd8Yc3/dTp/9l5WVhTFjxmDy5MmYNWtWk+uaev81p7U/+4baN7TcnMybNw9nzpzBn3/+2WS78PBwhIeH657HxMQgPT0d77//Pu68805jl9lqY8eO1X3fq1cvxMTEoHPnzti8eTMWLFjQ4DqWuP8A7X8ex44dW+dIwe0sbf81Rp/PQ2N/hjIMtdK8efMwZcqUJtuEhoa2aFv+/v71JoAVFRVBpVLVS8G3rqNUKlFUVFRndCg3NxdDhgxp0fu2lj593rhxI7y9vTFp0qRWv19AQABCQkJw6dKlVq+rj7bs09qzpi5fvtxgGKo98yUnJwcBAQG65bm5uY3uY0Nrbf+ysrIwcuRIxMTE4LPPPmv1+7X3/muMXC6Hvb19vf89NvWz9/f3b7C9g4NDk2HXlJ5//nn89NNPOHjwIIKCglq9/uDBg7FlyxYjVGZ4zs7O6NWrV6O/W5a4/wDg+vXr+PXXX/H999+3el1L2n/6fh42tl8N+RnKMNRKcrkccrncINuKiYnB22+/jezsbN0vxr59+yCVShEVFdXgOlFRURCLxYiPj8fDDz8MAMjOzsa5c+ewatUqg9R1u9b2WRAEbNy4EU888QTEYnGr36+goADp6el1/liMqS379NSpUwDQaK1hYWHw9/dHfHw8+vXrB0A7N+DAgQN477339Cu4lVrTv8zMTIwcORJRUVHYuHEj7OxafyS9vfdfYyQSCaKiohAfH4/7779ftzw+Ph733ntvg+vExMTg559/rrNs3759iI6O1ut32ZgEQcDzzz+PnTt3IiEhAWFhYXpt59SpUybfVy2lUCiQnJyMYcOGNfi6Je2/W23cuBG+vr4YP358q9e1pP2n7+dhTEwM4uPj64zM79u3z7ADAAabik31XL9+XTh16pSwfPlywcXFRTh16pRw6tQpoaysTBAEQaipqREiIyOFu+++W/jrr7+EX3/9VQgKChLmzZun20ZGRoYQHh4uHDt2TLds9uzZQlBQkPDrr78Kf/31l3DXXXcJffr0EWpqatq9jw359ddfBQDChQsXGnw9PDxc+P777wVBEISysjJh4cKFwuHDh4XU1FRh//79QkxMjNChQwehtLS0Pctu1uHDh4UPPvhAOHXqlHD16lVh+/btQmBgoDBp0qQ67W7tnyAIwsqVKwV3d3fh+++/F86ePSs8+uijQkBAgNn1LzMzU+jSpYtw1113CRkZGUJ2drbucStL2n/btm0TxGKxEBcXJ1y4cEGYP3++4OzsLFy7dk0QBEFYvHixMG3aNF37q1evCk5OTsJLL70kXLhwQYiLixPEYrHw3XffmaoLjZozZ47g7u4uJCQk1NlXlZWVuja392/16tXCzp07hb///ls4d+6csHjxYgGAsGPHDlN0oVkLFy4UEhIShKtXrwpHjx4VJkyYILi6ulrF/qulVquFjh07Cq+88kq91yxx/5WVlen+rQOg+8y8fv26IAgt+zycNm1anTM+Dx06JNjb2wsrV64UkpOThZUrVwoODg7C0aNHDVY3w5ARTZ8+XQBQ77F//35dm+vXrwvjx48XHB0dBS8vL2HevHlCdXW17vXU1NR661RVVQnz5s0TvLy8BEdHR2HChAlCWlpaO/asaY8++qgwZMiQRl8HIGzcuFEQBEGorKwUYmNjBR8fH0EsFgsdO3YUpk+fblb9qXXy5Elh0KBBgru7uyCTyYTw8HBh6dKlQkVFRZ12t/ZPELSnky5dulTw9/cXpFKpcOeddwpnz55t5+qbt3HjxgZ/X2//P5Ol7b9169YJISEhgkQiEfr371/n1PPp06cLw4cPr9M+ISFB6NevnyCRSITQ0FDhk08+aeeKW6axfXXr797t/XvvvfeEzp07CzKZTPD09BTuuOMO4Zdffmn/4lvokUceEQICAgSxWCwEBgYKDzzwgHD+/Hnd65a8/2rt3btXACCkpKTUe80S91/t6f+3P6ZPny4IQss+D4cPH65rX+vbb78VwsPDBbFYLERERBg8AIoE4ebsMiIiIiIbxFPriYiIyKYxDBEREZFNYxgiIiIim8YwRERERDaNYYiIiIhsGsMQERER2TSGISIiIrJpDENERERk0xiGiIiIyKYxDBEREZFNYxgiIpuSl5cHf39/vPPOO7plx44dg0Qiwb59+0xYGRGZCu9NRkQ2Z9euXbjvvvtw+PBhREREoF+/fhg/fjzWrFlj6tKIyAQYhojIJj333HP49ddfMWDAAJw+fRqJiYmQyWSmLouITIBhiIhsUlVVFSIjI5Geno4TJ06gd+/epi6JiEyEc4aIyCZdvXoVWVlZ0Gg0uH79uqnLISIT4sgQEdkcpVKJgQMHom/fvoiIiMAHH3yAs2fPws/Pz9SlEZEJMAwRkc35xz/+ge+++w6nT5+Gi4sLRo4cCVdXV/z3v/81dWlEZAI8TEZENiUhIQFr1qzBl19+CTc3N9jZ2eHLL7/En3/+iU8++cTU5RGRCXBkiIiIiGwaR4aIiIjIpjEMERERkU1jGCIiIiKbxjBERERENo1hiIiIiGwawxARERHZNIYhIiIismkMQ0RERGTTGIaIiIjIpjEMERERkU1jGCIiIiKbxjBERERENu3/AdkRSpAklf2yAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x = np.linspace(-10, 10, 400)\n",
    "\n",
    "y = np.arctan(x)\n",
    "\n",
    "plt.plot(x, y, label=r'$\\arctan(x)$')\n",
    "\n",
    "plt.title('Arctangent Function')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('arctan(x)')\n",
    "\n",
    "plt.grid(True)\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "plt.ylim(-np.pi/2, np.pi/2)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "反余切函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x = np.linspace(-10, 10, 400)\n",
    "\n",
    "y = np.pi/2 - np.arctan(x)\n",
    "\n",
    "plt.plot(x, y, label=r'$\\text{arccot}(x)$')\n",
    "\n",
    "plt.title('Arccotangent Function')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('arccot(x)')\n",
    "\n",
    "plt.grid(True)\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "高数上册1-2页"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
